Sure, but even though an LLM is only a function that "acts" (outputs a word) when called, it could (if it weren't just an LLM!) use that opportunity to act to p

Sure, but even though an LLM is only a function that "acts" (outputs a word) when called, it could (if it weren't just an LLM!) use that opportunity to act to pursue some curiosity-based line of discussion. One limiting factor as far as curiosity goes isn't just that an LLM is a passive function, but also that it's just a statistical sequence-to-sequence machine (a transformer) - that's all that exists under the hood. It doesn't have any mechanism for innate traits to influence the generation process. All you could do would be to train that one mechanism it does have to mimic human responses judged to reflect curiosity about specific fine-tuning inputs.